%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP178-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:24:42 PM UTC 2026
% Result : Unsatisfiable 9.52s 6.17s
% Output : CNFRefutation 9.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 73 ( 73 unt; 0 nHn; 16 RR)
% Number of literals : 73 ( 72 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 119 ( 17 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(p09b_3,hypothesis,
greatest_lower_bound(identity,c) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09b_3) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(p09b_4,hypothesis,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09b_4) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(p09b_1,hypothesis,
greatest_lower_bound(identity,a) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p09b_1) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(prove_p09b,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p09b) ).
cnf(c_0_16,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion ).
cnf(c_0_17,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb ).
cnf(c_0_18,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
associativity_of_glb ).
cnf(c_0_19,hypothesis,
greatest_lower_bound(identity,c) = identity,
p09b_3 ).
cnf(c_0_20,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity ).
cnf(c_0_21,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_22,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_23,hypothesis,
greatest_lower_bound(a,b) = identity,
p09b_4 ).
cnf(c_0_24,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2 ).
cnf(c_0_25,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_26,hypothesis,
greatest_lower_bound(identity,greatest_lower_bound(c,X1)) = greatest_lower_bound(identity,X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_28,hypothesis,
greatest_lower_bound(a,greatest_lower_bound(b,X1)) = greatest_lower_bound(identity,X1),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_29,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(X2,identity),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_17]) ).
cnf(c_0_30,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_31,hypothesis,
greatest_lower_bound(identity,greatest_lower_bound(X1,c)) = greatest_lower_bound(identity,X1),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_32,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1 ).
cnf(c_0_33,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_34,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_27]) ).
cnf(c_0_35,hypothesis,
greatest_lower_bound(a,multiply(greatest_lower_bound(X1,identity),b)) = greatest_lower_bound(identity,multiply(X1,b)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1 ).
cnf(c_0_37,hypothesis,
least_upper_bound(c,greatest_lower_bound(identity,X1)) = c,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
greatest_lower_bound(identity,multiply(inverse(X1),X2)) = multiply(inverse(X1),greatest_lower_bound(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_21]),c_0_17]) ).
cnf(c_0_39,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,hypothesis,
greatest_lower_bound(a,multiply(greatest_lower_bound(identity,X1),b)) = greatest_lower_bound(identity,multiply(X1,b)),
inference(spm,[status(thm)],[c_0_35,c_0_17]) ).
cnf(c_0_41,plain,
multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X3))) = least_upper_bound(multiply(inverse(X1),X2),X3),
inference(spm,[status(thm)],[c_0_36,c_0_27]) ).
cnf(c_0_42,hypothesis,
least_upper_bound(c,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = c,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_39]),c_0_39]) ).
cnf(c_0_44,hypothesis,
greatest_lower_bound(identity,multiply(c,b)) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_19]),c_0_22]),c_0_23]) ).
cnf(c_0_45,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion ).
cnf(c_0_46,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub ).
cnf(c_0_47,hypothesis,
least_upper_bound(multiply(X1,c),greatest_lower_bound(X2,X1)) = multiply(X1,c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_43]) ).
cnf(c_0_48,hypothesis,
greatest_lower_bound(identity,inverse(multiply(c,b))) = inverse(multiply(c,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_44]),c_0_39]),c_0_39]) ).
cnf(c_0_49,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X3,greatest_lower_bound(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_50,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(greatest_lower_bound(X1,X2),X3))) = greatest_lower_bound(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_18]) ).
cnf(c_0_51,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,hypothesis,
least_upper_bound(multiply(X1,c),greatest_lower_bound(X1,X2)) = multiply(X1,c),
inference(spm,[status(thm)],[c_0_47,c_0_17]) ).
cnf(c_0_53,hypothesis,
multiply(c,multiply(b,inverse(multiply(c,b)))) = identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_48]),c_0_43]),c_0_20]),c_0_39]),c_0_44]),c_0_43]),c_0_20]) ).
cnf(c_0_54,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(least_upper_bound(greatest_lower_bound(X2,X1),X3),X4))) = greatest_lower_bound(X4,greatest_lower_bound(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_18]),c_0_49]) ).
cnf(c_0_55,hypothesis,
greatest_lower_bound(X1,greatest_lower_bound(X2,multiply(X1,c))) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_18]) ).
cnf(c_0_56,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,least_upper_bound(greatest_lower_bound(X2,X1),X3))) = greatest_lower_bound(X2,X1),
inference(spm,[status(thm)],[c_0_50,c_0_17]) ).
cnf(c_0_57,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,greatest_lower_bound(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_18]) ).
cnf(c_0_58,hypothesis,
greatest_lower_bound(identity,a) = identity,
p09b_1 ).
cnf(c_0_59,plain,
greatest_lower_bound(X1,multiply(X1,X2)) = multiply(X1,greatest_lower_bound(identity,X2)),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_60,hypothesis,
multiply(b,inverse(multiply(c,b))) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_53]),c_0_39]) ).
cnf(c_0_61,hypothesis,
greatest_lower_bound(X1,greatest_lower_bound(multiply(X1,c),X2)) = greatest_lower_bound(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]) ).
cnf(c_0_62,hypothesis,
greatest_lower_bound(identity,greatest_lower_bound(a,X1)) = greatest_lower_bound(identity,X1),
inference(spm,[status(thm)],[c_0_18,c_0_58]) ).
cnf(c_0_63,plain,
multiply(greatest_lower_bound(X1,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_17]) ).
cnf(c_0_64,hypothesis,
greatest_lower_bound(b,inverse(c)) = inverse(c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_48]),c_0_60]) ).
cnf(c_0_65,hypothesis,
greatest_lower_bound(X1,least_upper_bound(X2,multiply(X1,c))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_51]),c_0_59]),c_0_19]),c_0_39]) ).
cnf(c_0_66,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2 ).
cnf(c_0_67,hypothesis,
least_upper_bound(greatest_lower_bound(identity,X1),greatest_lower_bound(a,X1)) = greatest_lower_bound(a,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_62]),c_0_46]) ).
cnf(c_0_68,hypothesis,
greatest_lower_bound(identity,multiply(b,c)) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_21]) ).
cnf(c_0_69,hypothesis,
greatest_lower_bound(X1,multiply(least_upper_bound(X2,X1),c)) = X1,
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,hypothesis,
least_upper_bound(identity,greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
prove_p09b ).
cnf(c_0_72,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_18]),c_0_24]),c_0_55]),c_0_17]),c_0_23]),c_0_22]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP178-2 : TPTP v9.2.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 13:27:12 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 9.52/6.17 % Version : CSE_E---1.7
% 9.52/6.17 % Problem : theBenchmark.p
% 9.52/6.17 % SZS status Unsatisfiable for theBenchmark.p
% 9.52/6.17 % SZS output start CNFRefutation
% See solution above
% 9.61/6.22 % Total time : 4.361s
%------------------------------------------------------------------------------